Various Uses of Maps

A preamble to using ACBA Maps

The National Geographic magazine has an excellent article by Geoff McGee (12 October 2015) - How to Make Maps and Influence People. It provides a brief over view of the approaches uses to make their maps influential. Maps may or may not be beautiful, but they are always intended to make an impact, to focus the readers’ or viewers’ attention on something important.

An extract from the McGee article states:-

“Mode says the historical masters of persuasive maps, though, were the British during their imperial height, when maps helped promote the size, power, and presumable invincibility of a small island nation’s global empire. They used not just maps themselves, he says, but also visual and geographical tactics to shape the viewer’s perception.”

Before focussing on ACBA Maps, it is worthwhile considering how maps have developed over the millennia.

Maps have always been designed to influence their readers. The mechanisms employed to guide these create these influences are as important as the maps themselves. Pure beauty is an important factor but, by no means, the only one.

The evolution of maps has taken a long and winding road, according to the blog UnEarthLabs. It considers two artefacts which may have claims to the oldest maps known.

Figure 1- A cave painting from Turkey dated from about 6200 BC

This is thought to be a representation of a city layout from ancient Anatolia. It is 9 feet wide. There is scholarly disagreement as to whether it is truly a map.

There is more certainty about the stone tablet below, which about the size of a modern day iPhone and dates from around 600 BC.

Figure 2- Babylonian stone tablet

The blog suggests that the Babylonian tablet is as much a record of spiritual and cultural belief, as it is a map. Curiously, I suspect, that all maps have both spiritual and cultural influences irrespective of their primary purpose.

Maps have always centred on telling stories and influencing their readers. The map below is from the 14^th Century and is part of a world atlas referred to as the Catalan Atlas. It is based on Marco Polo’s travels. I was interested to see the extent to which this map included written information, pictures and images that we would now describe as pictograms. Distances and angles between known locations are distorted to allow for this “extra” information.

Figure 3 - Marco Polo's travels (Catalan atlas – 14^th Century)

The use of the compass sparked a shift back to geographical maps made for practical navigation. The magnetic properties of iron had been known in China from about 2 centuries BC, but their ability to point north and south consistently was not employed in map making until the Renaissance in Europe. This coincided with a period of intense exploration and provided the backdrop to one of the most important developments in mapping – the Mercator projection. This allowed the projection of the earth’s spherical surface onto to a flat surface consistently.

Figure 4 - the Mercator projection of the world (modern)

Of course this leads to strangely stretched and misshapen outlines of land masses at the poles. However any single point on a land mass is correct relative to its longitudinal position.

Refinements in Mapping

Everyday people were realizing that a map was an act of persuasion, a visual rhetoric. In 1553, gentry in Surrey, England, drew a map of the town’s central fields, to prove these were common lands—and that villagers thus should be allowed to graze animals there. However, in many respects the French were the leaders in this technology, especially when it came to the use of icons and pictograms.

Figure 5 - Early symbols for water crossings (France)

Francois de Dainville, in his Le Language des Geographes (1964, p. 162), compiled map symbols for various water crossings from historical European maps (1543-1777).

Figure 6 - Early symbols for fords (France)

By the late 19th century, the surge in mathematic reasoning and measurement technology made mapmaking explode. In France, the Cassini family crisscrossed the country to calculate its dimensions with precision never before seen. Their trick? Using “triangulation”—a bit of trigonometry—to let them stitch together thousands of measurements taken by peering through the new, high-tech “theodolite.” Breakthroughs in binocular lenses allowed surveyors to measure scores of miles at a glance. World maps became increasingly accurate.

Local mapping became deeply granular. The British Ordnance Survey began mapping the U.K. down to the square yard, and the German entrepreneur Karl Baedeker produced similarly nuanced maps of European cities. Tourists could now confidently tour foreign realms, their annually updated guides in hand, able to locate individual buildings, much like today’s citizens peering at Google Maps on their phones. Being prominent on a local map was valuable to merchants, so mapmakers in the U.S. sold the rights. “If you paid more, you’d get your building cited,” Short notes. “It was like advertising.”

Pictograms, the Key to Interpretation and Contours

Originally, the visual impact of maps was very direct. The map was both a picture with words to describe the detailed meaning of the image.

Figure 7 - Mercator World Map 1569

The above Mercator World Map from 1569 includes a good deal of explanatory text. There are also a range of small images which could be the equivalent of modern pictograms. However, there is no key or explanation of what they might represent. There is very little interpretation required of the reader. The visual impact is almost instant.

Over the centuries mapping has become much more subtle and capable of conveying a wide range of information or, in some cases, misinformation.

According to the Nielsen Norman Group: “In addition to conveying brand personality through color and style, icons must first and foremost communicate meaning in a graphical user interface. Icons are, by definition, a visual representation of an object, action, or idea. If that object, action, or idea is not immediately clear to users, the icon is reduced to mere eye candy.”

However, meanings are not universal. In order to create an effective icon, one must consider the context of usage—the environmental, societal, political, and psychological factors that contribute to the reason why they are using the icon in the first place.

Figure 8 - Icons in the 17th Century

In many cases mapping icons are self-explanatory. However, over time, icons have become more abstract and context dependent.

A map key is an inset on a map that explains the symbols, provides a scale, and usually identifies the type of map projection used. Technically, the key is part of the map legend. The key explains the symbols while the legend holds the key and other information.

Here is an extract of the information provided on the UK’s Ordnance Survey maps.

Figure 9 - Mapping symbols and their meanings (an Extract from the Ordnance Survey)

The majority of maps use colour (Figure 4) and pictograms (Figure 8) to depict physical features. The development of contour lines to illustrate topography came in the late 18^th and early 19^th centuries. Their history is rather tortuous – see Chasing the Line.

Contour lines are most frequently used in large scale maps like the UK’s Ordnance Survey Explorer and Landranger series. In this series, they are the faint red-brown lines drawn on a map connecting points of equal elevation above sea level, meaning if you physically followed a contour line, the elevation (height of the land) would remain the same. Contour lines show elevation and the shape of the terrain. They're useful because they illustrate the shape of the land surface on the map. In other words, contour lines show the topography of the land. Understanding contours is a skill that will allow you to look at a map and picture the hill, with depressions for streams, hills and thin mountain ridges, etc. Contour lines are pictorial, meaning they do not exist on the ground.

Consider a landscape as shown below, together with its associated map.

Figure 10 - A landscape and its associated OS map

A profile of a landscape can be shown by interpreting the contour lines as shown.

Figure 11 - An irregular hill and its profile from contour lines

Contours allow the map reader to visualise the landscape in 3 dimensions even though it is presented on a flat (two dimensional) surface.

Mathematicians will recognise that this representational approach can be extended beyond three dimensions. There can be real difficulties when seeking to represent this on a flat surface. However, the images of a black hole from NASA can be regarded as a pictorial representation of huge amounts of data which has been analysed logically.

Mapping the Night Sky

Since the distances between Earth and individual stars or galaxies are so huge, the mapping of the night sky might (in terms of distance from Earth) appear to be an obvious subject for consideration. Ethan Seigel’s article “How far away are the stars?” discusses the difficulties.

From the map maker’s perspective these difficulties are not solvable, because there is no correlation between position in the sky and distance from Earth. One near star or galaxy could easily hide a more distance one. This represents a fundamental distinction between mapping objects in the night sky and mapping the surface of the earth whether above or below the surface of the sea. We cannot generate a contour line of stars that are equidistant from the earth.

The mapping of the night sky is conceptually different from mapping the surface of the Earth.

Mapping the Sea Bed

Authoritative sources claim that 71% of the earth’s surface is covered by water. But delve a little further into this figure it becomes very difficult to define exactly what this statement means. Does it include ponds, rivers and lakes? What about seasonal floods or occasional lakes? Are the icecaps of the Artic and Antarctica included? No doubt there are valid answers to these questions, but they all fundamentally concern land and water’s presence in that context.

In contrast less than 20% of the earth’s oceans have been mapped in any detail. By detail I mean the shape and composition of ocean or sea beds. For comparison, we know far more about our nearest planetary neighbours.

This gap in our knowledge has been recognised for over a hundred years (The History of GEBCO), but the methodologies we use for mapping the earth’s land masses (essentially light waves), cannot be applied in water. We first started mapping the shapes of river floods using plumb lines. These were then extended to relatively shallow seas.

The advent of sonar in the mid-20^th century was a major advance for mapping shallow seas. There are major technical difficulties for interpreting sonar for deep oceans. Although satellite mapping has allowed fairly low-level resolution for the deep oceans, there is a need for far more detailed coverage. This need has been recognised and is being pursued actively by the organisation Seabed 2030.

Figure 12- Atlantic Ocean at low level resolution

Mapping Spreadsheets – Connection?

Google’s dictionary defines a map as ‘a diagrammatic representation of an area of land or sea showing physical features, cities, roads, etc.’ This seems overtly earth bound. Alternatively, Wikipedia offers ‘A map is a symbolic depiction emphasizing relationships between elements of some space, such as objects, regions, or themes. Many maps are static, fixed to paper or some other durable medium, while others are dynamic or interactive.’ This definition covers all the elements reviewed above, but how does it apply to spreadsheets. After all spreadsheets are already two dimensional. Why do we need a Map?

In reality, spreadsheets are always at least three dimensional. The rows and columns of the cell grid, together with their contents as shown to the user, represent two dimensions. The third dimension is represented by the formula that manipulates the contents of the cell. Microsoft has also introduced additional dimensions, for example cell comments.

With the exception of Array Formulae, the formulae in adjacent cells are nearly always slightly different to each other as one moves down (or occasionally across) the grid. The purpose of mapping spreadsheets is to identify which groups of formulae are conceptually the same and to map their location in relation to the whole spreadsheet.

Unlike Microsoft’s formula auditing functionality, it does NOT attempt to demonstrate logical connection between the cell locations used within the formula, rather it highlights whether formulae are grouped together or in separate locations. The map helps highlight the conceptual logic of the spreadsheet.

Downloading ACBA Mapping

The ACBA-Mapping software is distributed as an Excel Add-In and can be downloaded from the link.

For those not familiar with handling Excel Add-Ins, instructions on what to expect and where to load your Add-Ins can be found at Generating the "ACBA-Mapping" Add-In.

Access to Help

There is a discussion group dedicated to providing a forum for help and information - Excel - Cell Mapping. I recommend you join the group.

Alternatively, you can email me directly from the Stephen Allen link within the form.

Acknowledgements

Experts in Excel have offered their advice and I am very grateful for this. My thanks go to Patrick O'Beirne (Systems Modelling), Jan Karel Pieterse (JKP Application Development Services) and Hans Hallebeek (HC & TS).

Spreadsheet Risks

Spreadsheet errors and inconsistencies is a subject that is of concern by professional developers as well as amateurs. The European Spreadsheet Risk Interest Group (EuSpRIG) considers the problems from an academic and professional perspective. The following links provide access to the EuSpRIG website and discussion forum.